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Modern Physics

An excursion into the

development of new ideas

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BBRThings to know

What is a black body

Sketch the spectrum of BB at different

temperatures

Note that

Wavelength at peak intensity (lmax)

decreases with increase temperature

Relationship lmaxis proportion to absolute

Temperature Wiens law (constant 2.898x10-3 m.K)

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Black Body Radiation

http://rh5.clemson.edu/ropermtn/naturalEM.php

Credits

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Total power per unit area is the area under the curve

This increases with temperature

Stefans law gives the relationship (P = eAs T4) I = sT4

Rayleigh-Jean Law

Attempt to derive spectral intensity by considering

standing waves in the cavity

Ultraviolet catastrophe (small wavelength)

Infinite total power

4

2),(

l

l

TkcTI B

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Plancks Solution

Assumptions Cavity Walls are oscillators

Oscillators have range of fundamental

frequencies Oscillators exchange radiation with cavity

Each oscillator of fund. Freq. f can absorb or

emit energy

E = n h f where n = 0,1,2,3

Novel Idea

Led to the correct eqn

1

2),(

5

2

Tk

hc

Be

hcTI

ll

l

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Photoelectric Effect

http://www.physics.umd.edu/perg/qm/qmcourse/NewModel/research

/pe_jcmst/Jcmst00.htm

Credits

http://www.physics.umd.edu/perg/qm/qmcourse/NewModel/researchhttp://www.physics.umd.edu/perg/qm/qmcourse/NewModel/research

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Classical Expectations

Light is a wave so its energy must dependon the intensity and independent of itsfrequency.

Emission of photoelectrons should notdepend on the frequency, but on theintensity

KE should depend on its intensity A delay should be expected as electrons

absorb enough energy from the wave

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Graphs

http://library.thinkquest.org/28383/nowe_teksty/htmla/1_8a.html

Credits

http://phycomp.technion.ac.il/~webteach/phys3/ph114053/adler/photo.html

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Observations

No current for frequency below threshold (Cutoff)

frequency. Independent of intensity

The amount of saturation current depends on the light

intensity

The maximum kinetic energy (or stopping voltage ) is

proportional to frequency, independent of intensity

Threshold frequency depends on the metal

Stopping voltage depends only on metal and frequency ,not on intensity

Instantaneous emission of electrons on illumination

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Conclusions

Light consists of discrete photons

Energy of a photon E = hf

Atom absorbs total photon Energy equal to the work function needed

to remove electron from atom

WF depends on the metal used Energy of photon in excess of WF goes

into K.E of electron (Cons. Of Energy)

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Compton Effect

Monochromatic X-rays scattered fromelectrons in Graphite

Observed change in wavelength which

varied with scattering angle (not expected)

)cos(112 ll cm

h

e

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Diagram

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Explanation

Light consists of discrete particles

These particles collide with the stationary

electrons of the graphite

Relativistic energy and momentum are

conserved (similar to particle-particle

collision)

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The Sun emits energy at a rate of 3.9x1026

W.(i) If the radius is 6.96x108 m, determinethe mean temperature.(ii) If the average

wavelength of its radiation is 550 nm,

determine the average number of photons

emitted by the sun in a second.

The wavelength associated with the cutoff

frequency of silver is 325 nm. Find themaximum kinetic energy and the stopping

potential for electrons emitted when silver is

illuminated by ultraviolet light of wavelength

Class Exercises

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Atomic Spectra Sunlight has continuous spectrum

When electric arc passed through gas, the gas

emits a line (emission) spectrum

White light passing through low density gas resultsin absorption spectrum

http://academic.kellogg.cc.mi.us/herbrandsonc/bio111/metabolism.htm

www.prophotolife.com

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Atomic Spectra

http://www.ruf.rice.edu/~mcannon/Research%20Home/Research%20Home%20Pictures/Spectrum.jpg

The Absorption and

emission spectraare characteristic of the

element.

Applications:Study of elements in The

Sun and Stars

Analysis of heavy metal

contamination in food

Neon Signs

Fluorescent lamps

http://www.ruf.rice.edu/~mcannon/Research%20Home/Research%20Home%20Pictures/http://www.ruf.rice.edu/~mcannon/Research%20Home/Research%20Home%20Pictures/

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Spectral Series of Hydrogen

RH is Rhdberg constant = 1.097373x107 m-1

nf = 2 Balmer series ( first observed and equation

deduced by school teacher)

nf = 1 Lyman series (UV range)

nf = 3 Paschen Series

Note ni > nf

Note n 0

Equation was empirical (not based on Theory)

22

111

if

Hnn

Rl

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Bohrs Postulates

Atom consists of electrons in circular orbits around

positive nucleus with Newtonian physics applying to

orbit.

The electron can only exist in stationary states. In these

states no energy is emitted

If an electron moves from one stationary state to that of

lower energy a photon is emitted with

E1 - E2 = h f (f is the frequency of the photon) The stationary states are such that angular momentum is

quantised mvr = n h/2(pi) n = 1,2,3,4,.

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Derivation of Bohrs atom

Coulomb Force Centripetal Acceleration

Energy E = PE + KE

Fourth Postulate

Obtain

rn = a n2

a = 52.92 pm En= 13.60 eV /n2

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Class Exercises

Determine the energy required to ionise a

hydrogen atom from the state n= 3. A

photon transitions from n=6 to n= 2.

Calculate the (i) Energy (ii) Wavelength ofthe emitted photon.

Discuss ground state, excited states

Draw the energy level diagram, theionisation energy and the first Bohr radius

for Singly ionised helium (-54.4eV n =1)

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Limitations of Bohr Atom

The Bohr Model

has flat circle but observation shows spherical

electronic orbit

Has minimum angular momentum of h/2

however Lmin = 0 Cannot explain spectra of more complex atoms

Cannot account for the variation of intensity or

splitting of spectral line under magnetic fields Cannot account for the wave nature of the

electron

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Nature of Light

Interference of light seemed conclusiveevidence for wave nature of light

Photoelectric effect discrete localised

energy Compton Effect proved localised p, E

Both confirm particle nature of light

Reduce light intensity in Youngsexperiment

Individual particles detected on screen

Conclude wave-particle duality for light

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De Broglie

Particle has a wavelength = h/p

Observed by Davisson Germer

Interference pattern observed for e, p, n, I2& buckyballs

Applications

Electron & Neutron diffraction used todetermine atomic structure liquids &solid

Electron diffraction used to study surfaces of

solids

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Class Exercises

In the typical television set the electrons

are accelerated through a potentialdifference of 25.0kV. Ignoring relativistic

effect, determine their De Broglie

wavelength and compare it to that of atennis ball served by Serena Williams

(m=56.7 g v= 120 mph)

1 mph = 0.447 m/s

p: www you u e com wa c v= e

http://www.youtube.com/watch?v=ZUI3lhRje_0http://www.youtube.com/watch?v=ZUI3lhRje_0

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p: www.you u e.com wa c v= e_

Observe Individual particles at detector

Low intensity area has low probabilityof particle

Interference pattern emerge over

time

Deduce e- detected as particles, but their

probability of arrival at a point on thescreen is determined by theinterference of a pair of waves

Image Credit

http://scienceblogs.com/startswithabang/upload/2009/05/

a_tale_of_two_slits/electron_two_slit.jpg

http://www.youtube.com/watch?v=ZUI3lhRje_0http://scienceblogs.com/startswithabang/upload/2009/05/http://scienceblogs.com/startswithabang/upload/2009/05/http://www.youtube.com/watch?v=ZUI3lhRje_0

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Complimentarity

The double slit experiment with reduced

particle number showed that the electron

is detected as a particle but their arrival at

a point on the screen is determined by theinterference of two waves.

Thus both wave and particle properties are

required to explain the particle.

Cannot observe both properties

simultanteously

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Cover one slit

No interference

http://www.youtube.com/watch?v=DfPeprQ7oGc

http://www.youtube.com/watch?v=DfPeprQ7oGchttp://www.youtube.com/watch?v=DfPeprQ7oGchttp://www.youtube.com/watch?v=DfPeprQ7oGc

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Quantum Mechanics

Matter wave?

Is complex

Has everything knowable about particle

Satisfy Schrdinger Equation

Interpretation of wave function

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Poetry in Physics Origin German

Erwin kann mit seinem Psi

kalkulieren wie noch nie.

Doch wird jeder gleich einsehn:

Psi lsst sich nicht recht verstehn

English translation that does not run as

smoothly, but may be easier to understand for

some. :-)

Erwin with his psi can docalculations quite a few.

But one thing has not been seen:

Just what does psi really mean?

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What Psi means

dxxdxxP2

)()(

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Review Standing Wave

Standing wave on a string of length L

l = 2L/n with n = 1,2,3

Note wavelengths are quantised For standing wave y = sin(kx)

Express y in terms of L & n

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Particle in a box

Particle in 1-D box with Infinitely hard walls Infinite potential well

Width of well L

Mass of particle m Particle exists only in certain stationary states

Stationary states are standing waves

Determines the possible wavelengths

L = ln/2 n = 1,2,3

The wave function is standing wave

Wave-function defines the probability distribution

of the particle

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Quantised Energy Levels

By DeBroglie the wavelength determines

the momentum

p determines KE for that state

Recall V= 0 so total E =

Derive E

Only quantised energy possible Note n 0 thus lowest energy state n = 1

ground state energy.

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Wave Function for PiB

Sketch

(x)

||2

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Class Exercises An electron is trapped in an infinite potential well

(particle in 1-D box) 250 pm wide and is in the

ground state. How much energy must it absorb if it is

to jump to the state n = 4. Determine the wavelength

of the photon emitted when it subsequently drops

back down to the n = 2 energy level.

A particle of mass m is in an infinite potential well of

width L. The particle is in the first excited state. Findthe ratio of the probability of finding the particle in a

small interval about point x = L/3 to that of finding

the particle in an interval of equal size around the

point x = L/4.

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Black Body Radiation

Temperature Wiens law

Stefans law

Plancks Solution

Photoelectric Effect

Experiment

Classical Expectations

Graphs

Observations

Einsteins Solution

Compton Effect

Experiment

Results

Explanation

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Atomic Spectra

Emission/Absorption

Spectral Series of Hydrogen Bohrs Postulates

Bohrs atom

De Broglies Hypothesis Quantum Mechanics

Wave function

Wave function interpretation Particle in a box